New DES based on Elliptic Curves

Abstract

DES was published by the United States' National Bureau of Standards in January 1977 as an algorithm to be used for unclassified data. The algorithm had been used in banks for funds transfer security [2]. DES encryption was broken in 1999 by Electronics Frontiers Organization. This resulted in NIST issuing a new directive that year so Triple DES that is three consecutive applications of DES was appeared but as DES became unsecured, researchers proposed a variety of alternative designs, which started to appear in the late 1980s and early 1990s: examples include RC5, Blowfish and IDEA. Most of these designs kept the 64-bit block size of DES; DES itself can be adapted and reused in more secure schemes [3]. In 2001, after an international competition, NIST selected a new cipher, the Advanced Encryption Standard (AES), as a replacement. The algorithm which was selected as the AES was submitted by its designers under the name Rijndael. Other finalists in the NIST AES competition included RC6 and Twofish. In our study, we will go back to the past and try to bring back DES to life by using elliptic curves which are considered the simplest possible curves after lines and conics. Elliptic curves over finite fields provide an inexhaustible supply of finite abelian groups. Such curves involve elementary